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A152077
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Length of the trajectory of the map x->A003132(x) started at x=n^2 up to the end of its first period.
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1
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1, 8, 12, 8, 11, 16, 5, 12, 11, 2, 18, 13, 17, 17, 13, 11, 11, 11, 13, 9, 13, 14, 11, 11, 11, 19, 12, 5, 12, 12, 17, 14, 15, 17, 13, 14, 17, 6, 4, 9, 14, 14, 16, 17, 13, 9, 9, 11, 14, 11, 15, 14, 11, 14, 11, 14, 11, 7, 13, 16, 17, 12, 15, 7, 6, 4, 18, 15, 14, 5, 9, 10, 12, 16, 13, 15, 12, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This accumulates the length of the "transient" or "pre-periodic" part of the
trajectory started at n^2 plus the length of the first period.
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FORMULA
| a(n) = A099645(n^2)+A031176(n^2) .
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EXAMPLE
| a(5)=11 since the trajectory starting at x=5^2 is 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58 the next term 89 is already there.
a(10)= 2 since the trajectory starting at x=10^2 is 100,1 and the next term is again the 1.
a(11)= 18 because the trajectory is 121, 6, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, the next 89 is already there.
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CROSSREFS
| Cf. A031176, A160862.
Sequence in context: A166173 A014453 A160862 * A173461 A143813 A143845
Adjacent sequences: A152074 A152075 A152076 * A152078 A152079 A152080
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KEYWORD
| nonn,base
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 16 2009
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